6.3 Factoring Trinomials and Perfect Square Trinomial BobsMathClass.Com Copyright © 2010 All Rights Reserved Write all possible pairs of factors of “a” and “c” 1. Factor the greatest common factor from the trinomial if possible. If the first term is negative, factor out the negative along with the gcf. 3.Observe the last sign of the trinomial. A)If the last sign of the trinomial is a a “+”, find a combination of products using factors from “a” and “c” which will add to obtain the coefficient of the middle term. B)If the last sign is a “–”, find a combination of products using factors from “a” and “c” which will subtract to obtain the coefficient of the middle term. C)Apply the “+” and “–” signs in order to obtain the coefficient of the middle term. If no combination will work, then the trinomial is “not factorable”. 4.Write the two sets of parentheses. Place the two factors of “a” in the first positions (order does not matter). Attach the variable being used in the problem next to each factor. Do not write in the signs yet. 5. Place the second pair of numbers in the last positions of each set of parentheses so that the order of multiplication is preserved (from step 3) Combination means to multiply a factor of the first pair by a factor of the second pair. Then multiply the remaining factor of the first pair with the remaining factor of the second pair. 6.Place the signs as was determined in Step Check by FOIL Method.

6.3 Factoring Trinomials and Perfect Square Trinomial BobsMathClass.Com Copyright © 2010 All Rights Reserved. 2 – + –7 1.The trinomial has no common factor 2.Find the factors of “a” and “c” Since the last sign is a minus, find the combination which will subtract to equal 7. Attach the “+” or “–” symbols so their difference is equal to the coefficient of the middle term. 4. Write two sets of parentheses with the first pair in the first positions. Also attach the variable being used in the trinomial. (3x )(4x ) 5. Place the second pair of numbers in the last positions of each set of parentheses so that the order of multiplication is preserved (from step 3) Place the signs in so that the product will result in the desired trinomial. (Use the + and – from step 3 to help place the signs.) – + 7.Check by FOIL Method. (Not Shown) Your Turn Problem #1

6.3 Factoring Trinomials and Perfect Square Trinomial BobsMathClass.Com Copyright © 2010 All Rights Reserved. 3 – – –11 1.Factor out the greatest common factor 2.Find the factors of “a” and “c” Since the last sign is a plus, find the combination which will add to equal –11. Both signs must be “–”. Their sum is negative and their product is positive. 4. Write two sets of parentheses with the first pair in the first positions. Also attach the variable being used in the trinomial. (2x )(3x ) 5. Place the second pair of numbers in the last positions of each set of parentheses so that the order of multiplication is preserved (from step 3) Place the signs in so that the product will result in the desired trinomial. (Use the + and – from step 3 to help place the signs.) Also, write GCF in front of factors. – – 7.Check by FOIL Method. (Not Shown) Your Turn Problem #2

6.3 Factoring Trinomials and Perfect Square Trinomial BobsMathClass.Com Copyright © 2010 All Rights Reserved. 4 Let’s look at the product of the two following binomials: using the square of the variable in both the first positions of the parentheses. – + –11 1.No common factor to factor out. 2.Find the factors of “a” and “c” Since the last sign is a minus, find the combination which will subtract to equal 11. Attach the “+” or “–” symbols so their difference is equal to the coefficient of the middle term. 4. Write two sets of parentheses with the first pair in the first positions. Also attach the square of the variable being used in the trinomial. (2x 2 )(3x 2 ) 5. Place the second pair of numbers in the last positions of each set of parentheses so that the order of multiplication is preserved (from step 3) Place the signs in so that the product will result in the desired trinomial. (Use the + and – from step 3 to help place the signs.) + – 7.Check by FOIL Method. (Not Shown) Your Turn Problem #3

6.3 Factoring Trinomials and Perfect Square Trinomial BobsMathClass.Com Copyright © 2010 All Rights Reserved. 5 – – –12 1.No common factor. 2.Find the factors of “a” and “c” Since the last sign is a plus, find the combination which will add to equal –12. Both signs must be “–”. Their sum is negative and their product is positive. 4. Write two sets of parentheses with the first pair in the first positions. Also attach the variable being used in the trinomial. (2x )(2x ) 5. Place the second pair of numbers in the last positions of each set of parentheses so that the order of multiplication is preserved (from step 3) Place the signs in so that the product will result in the desired trinomial. (Use the + and – from step 3 to help place the signs.) Also, write GCF in front of factors. – – 7.Check by FOIL Method. (Not Shown) Your Turn Problem #4

6.3 Factoring Trinomials and Perfect Square Trinomial BobsMathClass.Com Copyright © 2010 All Rights Reserved. 6 In the last example, we factored the polynomial 4x x + 9. The result was (2x - 3) 2, an example of a binomial squared. Any trinomial that factors into a single binomial squared is called a perfect square trinomial. Perfect Square Trinomials. So if the first and last terms of our polynomial to be factored are can be written as expressions squared, and the middle term of our polynomial is twice the product of those two expressions, then we can use these two previous equations to easily factor the polynomial. a 2 + 2ab + b 2 = (a + b) 2 a 2 – 2ab + b 2 = (a – b) 2 Next Slide

6.3 Factoring Trinomials and Perfect Square Trinomial BobsMathClass.Com Copyright © 2010 All Rights Reserved. 7 Since the first term, 16x 2, can be written as (4x) 2, and the last term, y 2 is obviously a square, we check the middle term. Your Turn Problem #5 The End. B.R xy = 2(4x)(y) (twice the product of the expressions that are squared to get the first and last terms of the polynomial)